






from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)
class        a       (					lowercase__  ):



      """simple docstring"""


      def __init__( self   :     Optional[Any]						, __lowercase   :     Distribution						, __lowercase   :     Optional[int]=None						, __lowercase   :     Optional[int]=None						, __lowercase   :     Any=0   )				-> Union[str, Any]:
        __UpperCAmelCase				:      List[str]	 =    1.0 if scale is None else scale
        __UpperCAmelCase				:      Any	 =    0.0 if loc is None else loc

        super().__init__(__lowercase						, [AffineTransform(loc=self.loc						, scale=self.scale						, event_dim=__lowercase   )]   )
      @property
      def       UpperCAmelCase ( self   :     Optional[Any]   )				-> Tuple:
        return self.base_dist.mean * self.scale + self.loc
      @property
      def       UpperCAmelCase ( self   :     Union[str, Any]   )				-> Tuple:
        return self.base_dist.variance * self.scale**2




      @property
      def       UpperCAmelCase ( self   :     Any   )				-> Union[str, Any]:
        return self.variance.sqrt()


class        a       (					nn.Module  ):



      """simple docstring"""


      def __init__( self   :     Union[str, Any]						, __lowercase   :     int						, __lowercase   :     Dict[str, int]						, __lowercase   :     Callable[..., Tuple[torch.Tensor]]						, **__lowercase   :     int   )				-> None:
        super().__init__(**__lowercase   )
        __UpperCAmelCase				:      str	 =    args_dim
        __UpperCAmelCase				:      int	 =    nn.ModuleList([nn.Linear(__lowercase						, __lowercase   ) for dim in args_dim.values()]   )
        __UpperCAmelCase				:      List[str]	 =    domain_map




      def       UpperCAmelCase ( self   :     Union[str, Any]						, __lowercase   :     torch.Tensor   )				-> Tuple[torch.Tensor]:
        __UpperCAmelCase				:      Dict	 =    [proj(__lowercase   ) for proj in self.proj]

        return self.domain_map(*__lowercase   )


class        a       (					nn.Module  ):



      """simple docstring"""


      def __init__( self   :     Union[str, Any]						, __lowercase   :     Optional[int]   )				-> List[str]:
        super().__init__()
        __UpperCAmelCase				:      List[str]	 =    function




      def       UpperCAmelCase ( self   :     int						, __lowercase   :     List[Any]						, *__lowercase   :     Tuple   )				-> Any:
        return self.function(__lowercase						, *__lowercase   )


class        a       :



      """simple docstring"""


      a    :					type
      a    :					int
      a    :					Dict[str, int]
      def __init__( self   :     Optional[int]						, __lowercase   :     int = 1   )				-> None:
        __UpperCAmelCase				:      Dict	 =    dim
        __UpperCAmelCase				:      int	 =    {k: dim * self.args_dim[k] for k in self.args_dim}
      def       UpperCAmelCase ( self   :     int						, __lowercase   :     str   )				-> Dict:
        if self.dim == 1:
          return self.distribution_class(*__lowercase   )
        else:
          return Independent(self.distribution_class(*__lowercase   )						, 1   )
      def       UpperCAmelCase ( self   :     Union[str, Any]						, __lowercase   :     int						, __lowercase   :     Optional[torch.Tensor] = None						, __lowercase   :     Optional[torch.Tensor] = None						, )				-> Distribution:
        __UpperCAmelCase				:      Tuple	 =    self._base_distribution(__lowercase   )
        if loc is None and scale is None:
          return distr
        else:
          return AffineTransformed(__lowercase						, loc=__lowercase						, scale=__lowercase						, event_dim=self.event_dim   )
      @property
      def       UpperCAmelCase ( self   :     List[str]   )				-> Tuple:
        return () if self.dim == 1 else (self.dim,)
      @property
      def       UpperCAmelCase ( self   :     int   )				-> int:
        return len(self.event_shape   )
      @property
      def       UpperCAmelCase ( self   :     Optional[int]   )				-> float:
        return 0.0
      def       UpperCAmelCase ( self   :     Optional[Any]						, __lowercase   :     int   )				-> nn.Module:
        return ParameterProjection(
            in_features=__lowercase						, args_dim=self.args_dim						, domain_map=LambdaLayer(self.domain_map   )						, )
      def       UpperCAmelCase ( self   :     Optional[int]						, *__lowercase   :     torch.Tensor   )				-> str:
        raise NotImplementedError()




      @staticmethod
      def       UpperCAmelCase ( __lowercase   :     torch.Tensor   )				-> torch.Tensor:
        return (x + torch.sqrt(torch.square(__lowercase   ) + 4.0   )) / 2.0


class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Dict[str, int]							=      {"df": 1, "loc": 1, "scale": 1}
      a    :					type							=      StudentT
      @classmethod
      def       UpperCAmelCase ( cls   :     Optional[int]						, __lowercase   :     torch.Tensor						, __lowercase   :     torch.Tensor						, __lowercase   :     torch.Tensor   )				-> Any:
        __UpperCAmelCase				:      List[str]	 =    cls.squareplus(__lowercase   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
        __UpperCAmelCase				:      Tuple	 =    2.0 + cls.squareplus(__lowercase   )
        return df.squeeze(-1   ), loc.squeeze(-1   ), scale.squeeze(-1   )


class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Dict[str, int]							=      {"loc": 1, "scale": 1}
      a    :					type							=      Normal
      @classmethod
      def       UpperCAmelCase ( cls   :     int						, __lowercase   :     torch.Tensor						, __lowercase   :     torch.Tensor   )				-> Optional[int]:
        __UpperCAmelCase				:      str	 =    cls.squareplus(__lowercase   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
        return loc.squeeze(-1   ), scale.squeeze(-1   )


class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Dict[str, int]							=      {"total_count": 1, "logits": 1}
      a    :					type							=      NegativeBinomial
      @classmethod
      def       UpperCAmelCase ( cls   :     Dict						, __lowercase   :     torch.Tensor						, __lowercase   :     torch.Tensor   )				-> Any:
        __UpperCAmelCase				:      Optional[int]	 =    cls.squareplus(__lowercase   )
        return total_count.squeeze(-1   ), logits.squeeze(-1   )
      def       UpperCAmelCase ( self   :     int						, __lowercase   :     List[Any]   )				-> Distribution:
        __UpperCAmelCase ,					__UpperCAmelCase				:      Optional[Any]	 =    distr_args
        if self.dim == 1:
          return self.distribution_class(total_count=__lowercase						, logits=__lowercase   )
        else:
          return Independent(self.distribution_class(total_count=__lowercase						, logits=__lowercase   )						, 1   )




      def       UpperCAmelCase ( self   :     str						, __lowercase   :     Tuple						, __lowercase   :     Optional[torch.Tensor] = None						, __lowercase   :     Optional[torch.Tensor] = None   )				-> Distribution:
        __UpperCAmelCase ,					__UpperCAmelCase				:      Dict	 =    distr_args

        if scale is not None:
          # See scaling property of Gamma.
          logits += scale.log()

        return self._base_distribution((total_count, logits)   )










"""simple docstring"""





def 	lowerCamelCase__			(				_lowerCamelCase			:						float						,							_lowerCamelCase			:						float					) ->							float:

  if density <= 0:
    raise ValueError('Impossible fluid density'					)
  if bulk_modulus <= 0:
    raise ValueError('Impossible bulk modulus'					)

  return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
  import doctest

  doctest.testmod()




